75 people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was 90 less than 4 times the number of away team fans, How many home team and away team fans attended the game?

Question

Julia Adams · Accepted Answer

Home fans = 42, Away fans = 33

Let's set #H# as the number of home team fans and #A# as the number of away team fans. 75 people attended the game, and we know that everyone was either an #H# or an #A#, so we can say: #H+A=75# We're also told that the number of #H# was 90 less than four times #A#, which we can write as: #H=4A-90# I'm going to set the first equation equal to #H# and then set the two equations equal to each other (since they will both be solved for #H#): #H+A=75=>H=75-A# and so #75-A=4A-90# #5A=165# #A=33# and so we can take #H=75-A# and find #H#: #H=75-33=42#

Kennedy Adams · Answer

undefined There were 15 home team fans and 60 away team fans at the game.